This preview shows page 1. Sign up to view the full content.
Unformatted text preview: minutes and 7 seconds (which is 127 seconds) the period T = 1 (127) = 127 seconds. Hence, the
angular frequency is ω = 2π = 127 radians per second. Putting these two pieces of information
together, we have that y = 64 sin 127 t describes the y -coordinate on the Giant Wheel after t
seconds, assuming it is centered at (0, 0) with t = 0 corresponding to the point Q. In order to ﬁnd
an expression for h, we take the point O in the ﬁgure as the origin. Since the base of the Giant
Wheel ride is 8 feet above the ground and the Giant Wheel itself has a radius of 64 feet, its center
is 72 feet above the ground. To account for this vertical shift upward,4 we add 72 to our formula
for y to obtain the new formula h = y + 72 = 64 sin 127 t + 72. Next, we need to adjust things so
that t = 0 corresponds to the point P instead of the point Q. This is where the phase comes into
play. Geometrically, we need to shift the angle θ in the ﬁgure back π radians. From Section 10.2.1,
we know θ = ωt = 12...
View Full Document